Learn and Control while Switching: with Guaranteed Stability and Sublinear Regret

Over-actuated systems often make it possible to achieve specific performances by switching between different subsets of actuators. However, when the system parameters are unknown, transferring authority to different subsets of actuators is challenging due to stability and performance efficiency concerns. This paper presents an efficient algorithm to tackle the so-called "learn and control while switching between different actuating modes" problem in the Linear Quadratic (LQ) setting. Our proposed strategy is constructed upon Optimism in the Face of Uncertainty (OFU) based algorithm equipped with a projection toolbox to keep the algorithm efficient, regret-wise. Along the way, we derive an optimum duration for the warm-up phase, thanks to the existence of a stabilizing neighborhood. The stability of the switched system is also guaranteed by designing a minimum average dwell time. The proposed strategy is proved to have a regret bound of $\mathcal{\bar{O}}\big(\sqrt{T}\big)+\mathcal{O}\big(ns\sqrt{T}\big)$ in horizon $T$ with $(ns)$ number of switches, provably outperforming naively applying the basic OFU algorithm

Regret Bounds for LQ Adaptive Control Under Database Attacks (Extended Version)

This paper is concerned with understanding and countering the effects of database attacks on a learning-based linear quadratic adaptive controller. This attack targets neither sensors nor actuators, but just poisons the learning algorithm and parameter estimator that is part of the regulation scheme. We focus on the adaptive optimal control algorithm introduced by Abbasi-Yadkori and Szepesvari and provide regret analysis in the presence of attacks as well as modifications that mitigate their effects. A core step of this algorithm is the self-regularized on-line least squares estimation, which determines a tight confidence set around the true parameters of the system with high probability. In the absence of malicious data injection, this set provides an appropriate estimate of parameters for the aim of control design. However, in the presence of attack, this confidence set is not reliable anymore. Hence, we first tackle the question of how to adjust the confidence set so that it can compensate for the effect of the poisonous data. Then, we quantify the deleterious effect of this type of attack on the optimality of control policy by providing a measure that we call attack regret.Comment: 10 page

Safety-Aware Learning-Based Control of Systems with Uncertainty Dependent Constraints (extended version)

The problem of safely learning and controlling a dynamical system - i.e., of stabilizing an originally (partially) unknown system while ensuring that it does not leave a prescribed 'safe set' - has recently received tremendous attention in the controls community. Further complexities arise, however, when the structure of the safe set itself depends on the unknown part of the system's dynamics. In particular, a popular approach based on control Lyapunov functions (CLF), control barrier functions (CBF) and Gaussian processes (to build confidence set around the unknown term), which has proved successful in the known-safe set setting, becomes inefficient as-is, due to the introduction of higher-order terms to be estimated and bounded with high probability using only system state measurements. In this paper, we build on the recent literature on GPs and reproducing kernels to perform this latter task, and show how to correspondingly modify the CLF-CBF-based approach to obtain safety guarantees. Namely, we derive exponential CLF and second relative order exponential CBF constraints whose satisfaction guarantees stability and forward in-variance of the partially unknown safe set with high probability. To overcome the intractability of verification of these conditions on the continuous domain, we apply discretization of the state space and use Lipschitz continuity properties of dynamics to derive equivalent CLF and CBF certificates in discrete state space. Finally, we present an algorithm for the control design aim using the derived certificates